Magnetotunnelling transport phenomena and quantum chaos in semiconductor heterostructures

The energy levels and eigenfunctions of the electronic motion in a wide potential well with a large tilted magnetic field have been calculated in the regime of strong classical chaos. Periodic modulations of the density of states due to level clustering are identified and related to the occurrence of distinct unstable periodic classical orbits. Individual periodic orbits are found to “scar” the wave functions corresponding to regular subsets of energy levels determined by quantizing the classical action. Resonant tunnelling spectroscopy provides a mean of investigating the link between the classical and quantum pictures of the motion. The tunnelling rates into scarred states are found to be much greater than the rates into nearby unscarred states. Owing to level broadening present experimental results do not distinguish between tunnelling into a discrete scarred state and tunnelling into a cluster of closely spaced levels. Further tunnelling experiments on double-barrier structures with narrower wells in higher magnetic fields will provide an accessible means of studying wave function scarring.